While there can be many aesthetic modifications, a normal Newton's cradle has a very simple setup: Several balls are hung in a line from two crossbars that are parallel to the line of the balls. These crossbars are mounted to a heavy base for stability.
On small cradles, the balls are hung from the crossbars by light wire, with the balls at the point of an inverted triangle. This ensures that the balls can only swing in one plane, parallel to the crossbars. If the ball could move on any other plane, it would impart less energy to the other balls in the impact or miss them altogether, and the device wouldn't work as well, if at all.
All the balls are, ideally, exactly the same size, weight, mass and density. Different-sized balls would still work, but would make the demonstration of the physical principles much less clear. The cradle is meant to show the conservation of energy and momentum, both of which involve mass. The impact of one ball will move another ball of the same mass the same distance at the same speed. In other words, it'll do the same amount of work on the second ball as gravity did on the first one. A larger ball requires more energy to move the same distance -- so while the cradle will still work, it makes it more difficult to see the equivalence.
As long as the balls are all the same size and density, they can be as big or as small as you like. The balls must be perfectly aligned at the center to make the cradle work the best. If the balls hit each other at some other point, energy and momentum is lost by being sent in a different direction. There's usually an odd number of balls, five and seven being the most common, though any number will work.
So now that we've covered how the balls are set up, let's look at what they're made of and why.